Numeracy

Percentage Change: Increase and Decrease




Percentage change is a useful concept for comparing increases and decreases in values. Here's how to calculate and interpret percentage change, with real-life examples.

Key Formulas for Percentage Change

  1. Percentage Increase:
    [
    \% { increase} = \frac{{New Number} - {Original Number}} / {{Original Number}} * 100
    ]

  2. Percentage Decrease:
    [
    \% { decrease} = \frac{{Original Number} - {New Number}} / {{Original Number}} * 100
    ]

Examples: Percentage Increase

Scenario: Dylan worked 35 hours in January and 45.5 hours in February.
- Step 1: Calculate the increase:
[
45.5 - 35 = 10.5 { hours increase.}
]

  • Step 2: Divide the increase by the original value:
    [
    10.5 \div 35 = 0.3
    ]

  • Step 3: Multiply by 100:
    [
    0.3 * 100 = 30\%.
    ]
    Result: Dylan worked 30% more hours in February.

Examples: Percentage Decrease

Scenario: Dylan worked 45.5 hours in February and 35 hours in March.
- Step 1: Calculate the decrease:
[
45.5 - 35 = 10.5 { hours decrease.}
]

  • Step 2: Divide the decrease by the original value (February):
    [
    10.5 \div 45.5 = 0.23
    ]

  • Step 3: Multiply by 100:
    [
    0.23 * 100 = 23\%.
    ]
    Result: Dylan worked 23% fewer hours in March compared to February.

Important: The percentage increase and decrease are not equal because the calculations are based on different starting values.

Calculating Values from Percentage Change

You can also calculate actual values if percentage change and one reference value are known.

Example 1: Rainfall Above Average

"Rainfall was 23% above the average, and the average rainfall is 250mm. What was the total rainfall?"

  • Step 1: Calculate 1% of the average:
    [
    250 \div 100 = 2.5 { mm.}
    ]

  • Step 2: Multiply by 23 to find the increase:
    [
    2.5 * 23 = 57.5 { mm.}
    ]

  • Step 3: Add the increase to the average:
    [
    250 + 57.5 = 307.5 { mm.}
    ]
    Result: The total rainfall was 307.5mm.

Example 2: Calculating the Average Rainfall

"Rainfall was 320mm, which is 23% above the average. What is the average rainfall?"

  • Step 1: Total rainfall represents 123% of the average (100% + 23%).
    Divide the total by 1.23 to find the average:
    [
    320 \div 1.23 = 260.2 { mm.}
    ]

  • Step 2: Calculate the difference between total and average:
    [
    320 - 260.2 = 59.8 { mm.}
    ]
    Result: The average rainfall was 260.2mm, and 59.8mm more rain fell than average.

Real-World Applications of Percentage Change

  • Business: Determine sales growth or decline.
  • Finance: Track investment performance.
  • Weather: Analyze unusual climate patterns.
  • Crime Statistics: Compare trends in reported incidents.

Example:
A report shows a "100% increase in violent crime" in a small town. On inspection, the increase was from 1 incident to 2. Understanding absolute values avoids misleading conclusions.

Tips for Accurate Calculations

  1. Always compare values to the correct starting point (e.g., January vs. February).
  2. Use a calculator for accuracy with large or complex numbers.
  3. Interpret percentage changes carefully, especially with small datasets.

By mastering percentage change calculations, you’ll gain clarity and confidence in analyzing data, spotting trends, and making informed decisions.

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